Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

using namespace std;

int main()
{
  int N, A[1000];

  cin >> N;
  multiset< int > s;
  for(int i = 0; i < N; i++) {
    cin >> A[i];
    s.insert(A[i]);
  }


  double ret = 0.0;
  for(int i = 0; i < N; i++) {
    s.erase(s.find(A[i]));
    for(int j = 0; j < N; j++) {
      if(i != j) {
        s.erase(s.find(A[j]));
        ret = max(ret, double(*--s.end() + *--(--s.end())) / (A[i] - A[j]));
        s.insert(A[j]);
      }
    }
    s.insert(A[i]);
  }

  cout << fixed << setprecision(10) << ret << endl;
}